Question

asked Nov 6, 2020 174k views

1 Answer

ToddEmon · Answer 1 · 2020-11-10T04:26:36+0000

1) Destructive interference

The condition for constructive interference to occur is:

$\delta = m\lambda$ (1)

where

$\delta =|d_1 -d_2|$ is the path difference, with

d_1 is the distance of the point from the first source

d_2 is the distance of the point from the second source

m is an integer number

$\lambda$ is the wavelength

In this problem, we have

$d_1 = 78.0 m\\d_2 = 143 m\\\lambda=26.0 m$

So let's use eq.(1) to see if the resulting m is an integer

$\delta =|78.0 m-143 m|=65 m\\m=(\delta )/(\lambda)=(65 m)/(26.0 m)=2.5$

It is not an integer so constructive interference does not occur.

Let's now analyze the condition for destructive interference:

$\delta = (m+(1)/(2))\lambda$ (2)

If we apply the same procedure to eq.(2), we find

$m=(\delta)/(\lambda)-(1)/(2)=(65.0 m)/(26.0 m)-0.5=2$

which is an integer: so, this point is a point of destructive interference.

2) Constructive interference

In this case we have

$d_1 = 91.0 m\\d_2 =221.0 m$

So the path difference is

$\delta =|91.0 m-221.0 m|=130.0 m$

Using the condition for constructive interference:

$m=(\delta )/(\lambda)=(130.0 m)/(26.0 m)=5$

Which is an integer, so this is a point of constructive interference.

3) Destructive interference

In this case we have

$d_1 = 44.0 m\\d_2 =135.0 m$

So the path difference is

$\delta =|44.0 m-135.0 m|=91.0 m$

Using the condition for constructive interference:

$m=(\delta )/(\lambda)=(91.0 m)/(26.0 m)=3.5$

This is not an integer, so this is not a point of constructive interference.

So let's use now the condition for destructive interference:

$m=(\delta)/(\lambda)-(1)/(2)=(91.0 m)/(26.0 m)-0.5=3$

which is an integer: so, this point is a point of destructive interference.

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